Rational points on elliptic curves

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1. Karrot_KreamJan 2023
   Subsequently, if you've taken an undergraduate level algebra class (or just have mathematical maturity and can work through some algebraic definitions) I suggest Tate and Silverman's Rational Points on Elliptic Curves. It's not super rigorous but it's good at introducing elliptic curves.

   https://link.springer.com/book/10.1007/978-3-319-18588-0

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2. hackerbluesOct 2010
   Anything written by Ian Stewart. "Rational points on elliptic curves" by Silverman
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3. DaniBAug 2021
   My Masters Thesis in 1972 was “Rational Points on Elliptic Curves”. It’s been sitting on my shelf for 50 years. A month ago, I discovered that EC’s are now the basis for encryption. Been fun exploring what’s been done since 1972. However, based on what I know, Cryptocurrencies are a dangerous scam. Way too many ways to cheat people who don’t have a clue what they are paying for.
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4. psykoticJul 2011
   I've seen you paste this a few times now and find myself disagreeing with parts of your framing.

   First, I don't know any mathematician personally who makes such a clear linguistic distinction between 'exercise' and 'problem'. Once you get to university-level mathematics, many exercises are problems in your sense but they still tend to be called exercises or something similar. If you insist on this terminological divide, I doubt most people will understand you.

   Secondly, there is the matter of an exercise's pedagogical purpose. Is it to sharpen general problem solving skills or to enlighten the student on a conceptual level? This goes beyond difficulty. It's a false dichotomy when stated so simply, but there is still something there. Many IMO-style problems are conceptually barren but still very tricky to solve. Conversely, some of my most enlightening learning experiences were solving guided sequences of exercises in a mathematical form of Socratic learning where none of the steps were individually too hard but still involving enough that they forced me to think and thus develop some insight on my own. (This approach can also fail. Silverman's otherwise excellent book Rational Points on Elliptic Curves has a guided proof of Bezout's theorem in the appendix that is just too atomized to engender much understanding.)

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